A Note on the Eigensystem of the Covariance Matrix of Dichotomous Guttman Items

We consider the covariance matrix for dichotomous Guttman items under a set of uniformity conditions, and obtain closed-form expressions for the eigenvalues and eigenvectors of the matrix. In particular, we describe the eigenvalues and eigenvectors of the matrix in terms of trigonometric functions o...

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Detalles Bibliográficos
Autores principales: Davis-Stober, Clintin P., Doignon, Jean-Paul, Suck, Reinhard
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Frontiers Media S.A. 2015
Materias:
Psychology
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4664651/
https://www.ncbi.nlm.nih.gov/pubmed/26648879
http://dx.doi.org/10.3389/fpsyg.2015.01767
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author Davis-Stober, Clintin P.
Doignon, Jean-Paul
Suck, Reinhard
author_facet Davis-Stober, Clintin P.
Doignon, Jean-Paul
Suck, Reinhard
author_sort Davis-Stober, Clintin P.
collection PubMed
description We consider the covariance matrix for dichotomous Guttman items under a set of uniformity conditions, and obtain closed-form expressions for the eigenvalues and eigenvectors of the matrix. In particular, we describe the eigenvalues and eigenvectors of the matrix in terms of trigonometric functions of the number of items. Our results parallel those of Zwick (1987) for the correlation matrix under the same uniformity conditions. We provide an explanation for certain properties of principal components under Guttman scalability which have been first reported by Guttman (1950).
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spelling pubmed-46646512015-12-08 A Note on the Eigensystem of the Covariance Matrix of Dichotomous Guttman Items Davis-Stober, Clintin P. Doignon, Jean-Paul Suck, Reinhard Front Psychol Psychology We consider the covariance matrix for dichotomous Guttman items under a set of uniformity conditions, and obtain closed-form expressions for the eigenvalues and eigenvectors of the matrix. In particular, we describe the eigenvalues and eigenvectors of the matrix in terms of trigonometric functions of the number of items. Our results parallel those of Zwick (1987) for the correlation matrix under the same uniformity conditions. We provide an explanation for certain properties of principal components under Guttman scalability which have been first reported by Guttman (1950). Frontiers Media S.A. 2015-12-01 /pmc/articles/PMC4664651/ /pubmed/26648879 http://dx.doi.org/10.3389/fpsyg.2015.01767 Text en Copyright © 2015 Davis-Stober, Doignon and Suck. http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
spellingShingle Psychology
Davis-Stober, Clintin P.
Doignon, Jean-Paul
Suck, Reinhard
A Note on the Eigensystem of the Covariance Matrix of Dichotomous Guttman Items
title A Note on the Eigensystem of the Covariance Matrix of Dichotomous Guttman Items
title_full A Note on the Eigensystem of the Covariance Matrix of Dichotomous Guttman Items
title_fullStr A Note on the Eigensystem of the Covariance Matrix of Dichotomous Guttman Items
title_full_unstemmed A Note on the Eigensystem of the Covariance Matrix of Dichotomous Guttman Items
title_short A Note on the Eigensystem of the Covariance Matrix of Dichotomous Guttman Items
title_sort note on the eigensystem of the covariance matrix of dichotomous guttman items
topic Psychology
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4664651/
https://www.ncbi.nlm.nih.gov/pubmed/26648879
http://dx.doi.org/10.3389/fpsyg.2015.01767
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